As the Barack Obama bandwagon began to roll in the run-up to the 2008 presidential election, we witnessed a striking example of the power of rhetoric. An inexperienced senator, riding pretty much on the strength of his oratorical fluency and fervour, swept past more established rivals to win first the Democratic nomination, then the White House.

I remember watching with wonderment a video of the "fired up, ready to go" speech he gave on the eve of voting, seeking inspiration as I wrestled with words during my own foray into political speechwriting. It is an astonishing performance, a witty exhortation forged by Obama's heritage, infused with passion and poetry and delivered with immense flair, way beyond anything attempted by modern British politicians. But the campaign also saw distrust of such dazzling wordplay. Hillary Clinton dismissed Obama as a man who "just gives speeches", while attacks from the right were so savage there was talk of a Republican "war on words".

As Sam Leith shows in You Talkin' to Me?, his romp through the art and history of rhetoric, there is a strong hostility to those with silver tongues dating back to Plato. It is seen as a device used by demons, a tool of demagogues and con artists. But of course, when John McCain and Sarah Palin complained of their rival's "verbage", their attacks were merely another rhetorical strategy. They just turned out to be less successful.

Leith points out that rhetoric is all around us. Far from being the preserve of politicians, it is the art of persuasion used in courtrooms and classrooms, battlefields and boardrooms. It is the careful choice of words used to ditch a lover, ask for a better table in a restaurant or plead with the kids to eat their cabbage. And you know what a rhetorical question is, don't you?

For hundreds of years, it was one of the key elements of education. In Shakespeare's day, rhetoric – learned by rote – comprised one-third of a basic schooling. Pupils were expected to memorise wise sayings and study the techniques of Aristotle and Ovid. Only in the 19th century did it begin to fall from favour, replaced by more scientific disciplines.

Leith attempts to reclaim rhetoric with a breezy book that sprays around examples from history, politics and popular culture to outline the building blocks of public speech, flitting happily from Cicero to J-Lo, from Hitler to Homer Simpson. Perhaps a little too happily – the cast of characters flash by almost too frequently, while the mixture of colloquialism and the classics sometimes jars. Mark Antony and the Australian rock band AC/DC are not obvious bedfellows, for example.

Despite this, when given time to breathe, Leith's often engaging examples lighten any sense of learning. The address by Colonel Tim Collins on the eve of the Iraq war is often held up as one of the most stirring modern pieces of military oratory, with its fine orotundities and vivid sense of history. But as one officer told Leith a few months later, teenage troops facing the threat of death "don't want to hear all that bollocks about Abraham and Isaac and the light of liberation". Good rhetoric relies on knowing your audience.

Then there is Edward Everett, chosen to dedicate a graveyard for the Union dead after the Battle of Gettysburg in the American civil war. He spent several months preparing, polishing and memorising his speech, then spoke for more than two hours with rolling classical allusions and an almost journalistic recalling of the fight. Afterwards, a late addition to the bill named Abraham Lincoln stepped up to make a few remarks in reply. In two minutes and barely 250 words, he delivered the most influential piece of rhetoric in American history.

Inevitably, many of the best examples come from politics, whether it is Churchill, whose bombastic prose – carefully crafted and rehearsed in front of mirrors – found its moment when the nation was under threat, or Ronald Reagan, fortunate to have the brilliant Peggy Noonan as his speechwriter. She was a true believer in the power of words to shape tribal identity, but also knew that a good speech relied on intense research and endless editing. Her skill with words and ability with literary techniques helped turned a B-movie actor into an A-grade orator.

Pithanon tini pithanon, as Aristotle told us. "What is convincing is what one can be convinced by." Ian Birrell

Ian Birrell is a former speechwriter for David Cameron. . Sam Leith and Mary Beard will be at Kings Place in London to talk about rhetoric on Wednesday 26 October. For more information, go to theguardian.com/extra